Robotics: Science and Systems I

Single-Cluster Spectral Graph Partitioning
for Robotics Applications

Edwin Olson, Matthew Walter, Seth Teller, John Leonard

Abstract: We present SCGP, an algorithm for finding a single
cluster of well-connected nodes in a graph. The general problem
is NP-hard, but our algorithm produces an approximate solution
in O(N2) time by considering the spectral properties of the
graph's adjacency matrix. We show how this algorithm can be
used to find sets of self-consistent hypotheses while rejecting
incorrect hypotheses, a problem that frequently arises in robotics.
We present results from a range-only SLAM system, a polynomial
time data association algorithm, and a method for parametric line
fitting that can outperform RANSAC.